Tomoyuki ICHIBA

Associate Professor, Department of Statistics & Applied Probability and Center for Financial Mathematics and Actuarial Research, and Mathematics in College of Creative Studies

at University of California Santa Barbara

Current Research


(1) ``Large deviations for interacting Bessel-like processes and applications to systemic risk" (with M. Shkolnikov) arXiv1303.3061

(2) ``Convergence and stationary distribution for Walsh diffusions'' arXiv: 1706.07127 (with Andrey Sarantsev).

(3) ``Option pricing with delayed information'' arXiv: 1707.01600 (with Seyyed Mostafa Mousavi).

(4)``An Infinite-dimensional McKean-Vlasov stochastic equation'' arXiv: 1805.01962 (with Nils Detering and Jean-Pierre Fouque).

Recently Published Papers

[13] ``Stochastic integral equations for Walsh semimartingales" Annales de l'Institut Henri Poincare (2018) Vol. 54, No. 2, 726-756 (with Ioannis Karatzas, Vilmos Prokaj and Minghan Yan) arXiv: 1505.02504

[12] ``Yet another condition for absence of collisions for competing Brownian particles'' Electronic Communications in Probability Volume 22 (2017), paper no. 8, 7 pp. (with Andrey Sarantsev) arXiv:1608.07220 .

[11] ``Skew-unfolding the Skorokhod reflection of a continuous semimartingale" Stochastic Analysis and Applications 2014 In Honor of Terry Lyons. Springer Proceedings in Mathematics & Statistics (2014) 349-376 (with Ioannis Karatzas) arXiv: 1404.4662.

[10] ``Planar diffusions with rank-based characteristics and perturbed Tanaka equations" Probability Theory and Related Fields 156 (2013) 343-374; a full version with additional topics of Transition probabilities, Time reversibility and Maximality is also available in (with E. R. Fernholz, V. Prokaj and I. Karatzas) arXiv:1108.3992 .

[9] ``Strong solutions of stochastic equations with rank-based coefficients" Probability Theory and Related Fields 156 (2013) 229-248 (with I. Karatzas and M. Shkolnikov) arXiv1109.3823 .

[8] ``Diffusions with rank-based characteristics and values in the nonnegative quadrant" Bernoulli 19 (2013) 2455-2493 (with Ioannis Karatzas and Vilmos Prokaj) arXiv:1202.0036.

[7] ``Convergence rates for rank-based models with applications to portfolio theory" Probability Theory and Related Fields 156 (2013) 415-448 (with S. Pal and M. Shkolnikov) arXiv:1108.0384.

[6] ``A second-order stock market model" Annals of Finance 9 (2013), 439-454 (with R. Fernholz and I. Karatzas) arXiv:1302.3870.

[5] ``Two Brownian particles with rank-based characteristics and skew-elastic collisions'' Stochastic Processes and their Applications 123 (2013) 2999-3026 (with E. Robert Fernholz and Ioannis Karatzas) arXiv:1206.4350 .

[4] ``Stability in a model of inter-bank lending" SIAM Journal of Financial Mathematics 4 (2013) 784-803 (with J-P. Fouque).

[3] ``Hybrid Atlas models" Annals of Applied Probability 21 no 2. (2011), 609-644. (with R. Fernholz, I. Karatzas, A. Banner and V. Papathanakos) arXiv:0909.0065.

[2] ``Collisions of Brownian particles" Annals of Applied Probability 20 no 3. (2010), 951-977 (with I. Karatzas) arXiv:0810.2149.

[1] ``Efficient estimation of one-dimensional diffusion first passage time densities via Monte Carlo simulation" Journal of Applied Probability 48 no 3. (2011) 699-712 (with Constantinos Kardaraz) arXiv:1008.1326.


``Topics in multi-dimensional diffusions: attainability, reflection, ergodicity and rankings'' Dissertation Columbia University. 2009. [924kb].

Conference Proceedings

[C4] ``Stochastic analysis for collision of Brownian particles'' March 2017 The Mathematical Society of Japan.

[C3] ``On mean-field approximation of particle systems with annihilation and spikes'' at Probability Symposium Dec. 2016, published in RIMS RIMS Kokyuroku Kyoto University, Kyoto, 2017.

[C2] `` Folding and Skew-Unfolding of One-dimensional Continuous Semimartingales" RIMS Kokyuroku No 1952: Symposium on Probability Theory, Kyoto 2014

[C1] ``On planar rank-based diffusions with skew-elastic collisions" RIMS Kokyuroku No 1903: Symposium on Probability Theory, Kyoto 2013


``Detecting Mean-field" Seminar on Stochastic Processes at Brown University (May 2018)

``Stochastic Integral Equations for Walsh Semimartingales" IMA Special Workshop: Reflected Brownian motions, Stochastic Networks and their applications at University of Minnesota (June 2015)

``Strong/Weak Solutions of 2D Diffusions with Rank-based Characterisits" Probabiliy, Control and Finance at Columbia University (May 2012)

Miscellaneous Papers of Statistics in Sports, Biology and Actuarial Science

(S4) ``Estimating the effect of the red card in soccer: when to commit an offense in exchange for preventing a goal opportunity'' Journal of Quantitative Analysis in Sports 5, no. 1 / 2009. (with Jan Vecer and Frantisek Kopriva).

(S3)``On probabilistic excitement of sports games.'' Journal of Quantitative Analysis in Sports 3, no. 6 / 2007. (with Jan Vecer and Mladen Laudanovic).

(S2) ``Assessing substitution variation across sites in grass chloroplast DNA.'' Journal of Molecular Evolution 64, no. 6 pp. 605-613 / June, 2007. (with Tian Zheng and Brian Morton) .

(S1) ``On multi-period statistical risk management methods and equity-linked life insurance.'' Journal of the Japan Statistical Society. Japanese issue 35, no. 2 pp. 103-123. / 2006. abstract. (with Naoto Kunitomo).

Last modified: August 2015.

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